Related papers: Order estimation of Markov chains
We consider the convergence of a continuous-time Markov chain approximation X^h, h>0, to an R^d-valued Levy process X. The state space of X^h is an equidistant lattice and its Q-matrix is chosen to approximate the generator of X. In…
Stochastic optimization in learning and inference often relies on Markov chain Monte Carlo (MCMC) to approximate gradients when exact computation is intractable. However, finite-time MCMC estimators are biased, and reducing this bias…
We consider MAP estimators for structured prediction with exponential family models. In particular, we concentrate on the case that efficient algorithms for uniform sampling from the output space exist. We show that under this assumption…
The paper is concerned with the equilibrium distributions of continuous-time density dependent Markov processes on the integers. These distributions are known typically to be approximately normal, and the approximation error, as measured in…
The definition of order indices for density matrices is extended to finite systems. This makes it possible to characterize the level of ordering in such finite systems as macromolecules, nanoclusters, quantum dots, or trapped atoms. The…
We consider Markovian models on graphs with local dynamics. We show that, under suitable conditions, such Markov chains exhibit both rapid convergence to equilibrium and strong concentration of measure in the stationary distribution. We…
The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding a…
We study continuous-time Markov chains on the non-negative integers under mild regularity conditions (in particular, the set of jump vectors is finite and both forward and backward jumps are possible). Based on the so-called flux balance…
Partially ordered sets of type (k, n) are the sets such that a) cardinality of each set is n, b) dimension of each set is two, c) length of the maximal antichain in each set is k. Let \alpha_k(n) be the number of partially ordered sets of…
We study a multivariate Markov chain on the symmetric group with remarkable enumerative properties. We conjecture that the stationary distribution of this Markov chain can be expressed in terms of positive sums of Schubert polynomials. This…
Verification of infinite-state Markov chains is still a challenge despite several fruitful numerical or statistical approaches. For decisive Markov chains, there is a simple numerical algorithm that frames the reachability probability as…
Markov chain Monte Carlo (MCMC) is a sampling-based method for estimating features of probability distributions. MCMC methods produce a serially correlated, yet representative, sample from the desired distribution. As such it can be…
We consider local alignments without gaps of two independent Markov chains from a finite alphabet, and we derive sufficient conditions for the number of essentially different local alignments with a score exceeding a high threshold to be…
The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It is common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention…
The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…
In this paper we investigate the kernel estimator of the density for a stationary reversible Markov chain. The proofs are based on a new central limit theorem for a triangular array of reversible Markov chains obtained under conditions…
In the continuity of a recent paper ([6]), dealing with finite Markov chains, this paper proposes and analyzes a recursive algorithm for the approximation of the quasi-stationary distribution of a general Markov chain living on a compact…
Let $E$ be a graph-directed set associated with a di-graph $G$. Let $\mu$ be a Markov-type measure on $E$. Assuming a separation condition for $E$, we determine the exact convergence order of the $L_r$-quantization error for $\mu$. This…
Almost sure convergence rates for linear algorithms $h_{k+1} = h_k +\frac{1}{k^\chi} (b_k-A_kh_k)$ are studied, where $\chi\in(0,1)$, $\{A_{k}\}_{k=1}^\infty$ are symmetric, positive semidefinite random matrices and $\{b_{k}\}_{k=1}^\infty$…
We consider a sequence of Markov chains $(\mathcal X^n)_{n=1,2,...}$ with $\mathcal X^n = (X^n_\sigma)_{\sigma\in\mathcal T}$, indexed by the full binary tree $\mathcal T = \mathcal T_0 \cup \mathcal T_1 \cup ...$, where $\mathcal T_k$ is…